Generalized
Local Maxwell Tomography for Mapping of Electrical Property Gradients and
Tensors

1Bernard
and Irene Schwartz Center for Biomedical Imaging, Department of Radiology,
New York University School of Medicine, New York, NY, United States; 2Sackler
Institute of Graduate Biomedical Sciences, New York University School of
Medicine, New York, NY, United States; 3Bernard and Irene Schwartz
Center for Biomedical Imaging, Department of Radiology, New York University,
New York, NY, United States; 4Cambridge Research Associates,
Newton, MA, United States

At last years ISMRM meeting, we introduced the Local
Maxwell Tomography (LMT) method for noninvasive mapping of the electrical
properties of tissue or materials.Here, we generalize the theory of LMT to encompass the electrodynamic
effects of a) non-vanishing spatial gradients of electrical properties, e.g.
at tissue boundaries, and b) structural anisotropies resulting in nontrivial
electrical property tensors.We
demonstrate that the generalized LMT framework eliminates edge artifacts
observed in simpler implementations.We also outline strategies by which tensor structure may be determined
if a sufficient number of measurements and coil elements are deployed,
potentially enabling electrical property tractography.